With　the　large-scale　integration　of　renewable　energy　(RE)　sources　and　rapid　advancements　in　smart　grid　(SG)　technologies,　the　efficient　integration　of　diverse　energy　resources　to　achieve　supply-demand　balance　and　maximize　cost-effectiveness　has　emerged　as　a　research　hotspot　in　the　energy　sector.　This　paper　addresses　the　real-time　scheduling　challenge　in　integrated　energy　systems　(IES)　within　the　context　of　SG,　emphasizing　pivotal　factors　such　as　electric　and　thermal　load　scheduling,　energy　storage　control,　dynamic　electricity　pricing,　carbon　emission　mechanisms,　and　demand　response　(DR).　To　this　end,　we　propose　a　comprehensive　scheduling　model　tailored　for　IES,　aiming　to　minimize　the　total　cost　over　the　dispatch　cycle.　Furthermore,　an　optimal　scheduling　algorithm　based　on　approximate　dynamic　programming　(ADP)　was　designed　to　solve　this　model.　Numerical　experiments　reveal　that,　while　ensuring　user　comfort,　the　proposed　real-time　scheduling　scheme,　by　comprehensively　considering　the　interactions　among　various　system　inputs,　significantly　enhances　system　flexibility　and　economic　performance.　It　effectively　tackles　the　uncertainty　of　RE,　thereby　improving　energy　utilization　efficiency.　©　2025　International　Academic　Press